A254070 - OEIS

A254070

a(n) = -1 + (3/2)^(-1 + v(1 + F(4*n - 3)))*(1 + F(4*n - 3)), where v(y) is the 2-adic valuation of y, F(x) = (3*x + 1)/2^v(3*x + 1), and x == 1 (mod 2).

1, 1, 17, 5, 13, 1, 29, 17, 25, 17, 161, 17, 37, 5, 65, 53, 49, 13, 125, 29, 61, 1, 101, 53, 73, 29, 269, 41, 85, 17, 137, 161, 97, 25, 233, 53, 109, 17, 173, 89, 121, 161, 1457, 65, 133, 17, 209, 161, 145, 37, 341, 77, 157, 5, 245, 125, 169, 65, 593, 89, 181, 53, 281, 485, 193, 49, 449, 101, 205, 13

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OFFSET

1,3

COMMENTS

a(n) is the first successor in the 3x+1 trajectory of 4*n-3 that is congruent to 1 mod 4. - Ruud H.G. van Tol, Jul 16 2023

LINKS

Ruud H.G. van Tol, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = 4*A257480(n) - 3. - L. Edson Jeffery, Mar 29 2021

MATHEMATICA

v[y_] := IntegerExponent[y, 2]; f[x_] := (3*x + 1)/2^v[3*x + 1]; s[n_] := -1 + (3/2)^(-1 + v[1 + f[4*n - 3]])*(1 + f[4*n - 3]); Table[s[n], {n, 70}] (* L. Edson Jeffery, Mar 29 2021 *)

PROG

(PARI) a(n) = my(x=3*n-2, v=valuation(x, 2)); x>>=v; v=valuation(x+1, 2)-1; ((x>>v)+1)*3^v-1; \\ Ruud H.G. van Tol, Jul 16 2023

CROSSREFS

Cf. A257480, A253676, A254068.

Sequence in context: A367356 A196924 A109215 * A297982 A298631 A338559

Adjacent sequences: A254067 A254068 A254069 * A254071 A254072 A254073

KEYWORD

nonn

AUTHOR

L. Edson Jeffery, May 03 2015

EXTENSIONS

New name by L. Edson Jeffery, Mar 29 2021

STATUS

approved